This research presents two novel
approaches for nonholonomic motion planning. The methodologies presented
are based on the standard Fast Marching Square path planning method and
its application to car-like robots. In the first method, the
environment is considered as a 3D C-Space, with the first two dimensions
given by the position of the robot, and the third dimension by its
orientation. This means we operate over the configuration space instead
of the bi-dimensional environment map. Besides, the trajectory is
computed along the C-Space taking into account the dimensions of the
vehicle, and thus guaranteeing the absence of collisions. The second
method uses the standard Fast Marching Square, and takes advantage of
the vector field of velocities computed in the first step of the method
in order to adapt the motion plan to the control inputs that a car-like
robot is able to execute. Both methods assure smoothness and safety of
the calculated paths and, besides, they provide the control plan to
perform the trajectory.
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